hectictar

Hello to you too! 👋

RS  =  RS ,   ∠RST = ∠RSQ ,   SQ  =  ST

Therefore,  △QRS ≅ △TRS  by the  SAS Congruence Postulate.

The coordinates of square ABCD are  A(0, 0) ,  B(a, 0) ,  C(a a) , and ​ D(0,  a) .

The slope of  AC   =   [a - 0] / [a - 0]   =   1 .

The slope of  BD   =   -1 .

The product of the slopes   =   1 * -1   =   -1 .

Angle  J  is the same as angle  X ,  so since  X  is listed last in the name, we must list  J  last.

XF  is the same length as  JL  , so the last two letters must be  LJ

Then the first letter must be  N .  So...

△NLJ   ≅   △PFX ​

slope of  EF   =   difference in  y  values / difference in  x  values

slope of  EF   =   [ -1 - -5 ] / [ -2 - -9 ]

slope of  EF   =   4 / 7

slope of a line perpendicular to  EF   =   - 7 / 4

There are a few ways to do this... here's one way..

Draw a rectangle around the triangle, so...

area of the triangle in question  =  area of the rectangle  -  area of the triangles around it

area of triangle in question   =   (4 * 6)  -  ( 1/2 * 4 * 4 )  -  ( 1/2 * 4 * 2 )

area of triangle in question   =   24  -  8  -  4   =   12   sq. units

When you double the  x  coordinates, it changes the shape of the triangle. So

△JKL is not congruent to △J'K'L' because the rules do not represent a sequence of rigid motions.

The slope of the line     -2x + 3y  =  6     is     2/3  .

The slope of the line     -3x − 2y  =  4     is    -3/2  .  This is perpendicular.

The slope of the line     -2x + 3y  =  -6    is     2/3  .  This is parallel.

The slope of the line      2x + 3y  =  6     is    -2/3  .  This is neither.

The slope of the line     -2x + 3y  =  0     is     2/3  .  This is parallel.

LOL! I just tried re-uploading it...seemed to work! 

Thanks CPhill!! That is weird...is the picture blocked for you? I don't think it was blocked last night!